球面穩(wěn)定同倫群中的若干新元素族.pdf

1、南開大學(xué)碩士學(xué)位論文球面穩(wěn)定同倫群中的若干新元素族姓名：劉秀貴申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：林金坤20030101AbstractThestablehornotopygroupisaveryimportantprobleminalgebraictopologyLetAbetheroodPSteenrodalgebraandSbethespherespectrumlocalizedatanoddprimePTodetermin

2、ethestablehomotopygroupsofspheres7rSisoneofthecentralproblemsinhomotopytheoryOneofthemaintoolsteachitistheAdamsspectralsequence(ASS)鹺’=Eztj。(名，磊)≥7Tt—sS，wherethe霹t_termisthecohomologyofAIfafamilyofhomotopygenerators矗in霹c

3、onvergesnontriviallyintheASS，thenwegetafamilyofhomotopyelements五in矸Sandwesaythat^isrepresentedbyXi∈霹1豐andhasfiltration8intheASSSofar，notSOmazlyfamiliesofhomotopyelementsin丌，ShavebeendetectedIn1981RCohendetectedafamily。一1

4、∈7■nq口一3Sfor饑≥2whichhasfiltration3intheASSandisrepresentedbyhob。一l∈EZtaA$“qq(％，乙)，whereq=2(p一1)Inthisthesis，wealsodetectsomefamiliesofhomotopyelementsin7r，SbyadoptingtwomethodsOneisnamedasgeometrymethod，theotherisnamedas

5、algebraicmethodInthisthesis，wedetectfournewfamiliesinthestableholnotopyofspheresThisthesiscontainsfivechaptersInthefirstchapter，wereviewthebackground，thedevelopmentsandresultsrelatingtotheproblemdiscussedinthisthesisInth

6、esecondchapter，bythegeometrymethodwedetectanewnontrivialfamilyinthestablehomotopyofspheresandprovethat廈2hn≠0∈EXtA如Ⅵ(舢’鯽(州)m(名，磊)isapermanentcycleintheASSanditconvergestoanontrivialelementoforderPin7r礦q十(s21pq(s1)日一3s，whe

7、reP25，n≥3，q=2∞一1)：0≤sP一2Inthecourseofproofanewfamilyofhomotopyelementsin7rV(1)whichisrepresentedby風(fēng)i7，i；(^。)∈ExtAp“。(’1)41(日K，乙)intheAdamsspectralsequenceisdetectedInthethird(：hap—ter，theforthchapterandthefifthchapter，by

8、thealgebraicmethodwedetectthatintheAdamsspectralsequence，s3hlk∈ExtA5礦4十‘3咿4‘3拙‘s十1)q5(Zp，乙)(p≥7，n≥4，0≤sP一3)，吼3(60hnhik—1)∈ExtA6pnq(sT3)p2q(s3)pq(s1)qs(磊，磊)(p≥7，禮≥4，0ssP一4)and廈2boh?！蔈xt蓋5礦9‘53’p?！?1’。。(乙，zP)(p≥5，n≥3，0曼sP一